Question

When two bodies , a heavy one and a light one are acted upon by the same force for the same time then :-
a)the light body builds up a lower velocity than the heavy one and the momentum gained is different in both the cases.
b)the light body builds up a higher velocity than the heavy one and the momentum gained is different in both the cases.
c)the light body builds up a higher velocity than the heavy one and the momentum gained is same in both the cases.


Please justify your answer also !!

Answer 1

Force = Rate of change of momentum or \(\sf Force = \huge \frac{\Delta mv}{t}\)

Answer 2

Here Force and time are constant

Answer 3

F = ma

Answer 4

the force of gravity will be differnt on both the objects ? the heavier one will accelerate faster ?

Answer 5

so \(\sf m\propto \frac{1}{v}\)

Answer 6

Heavier one will have less velocity

Answer 7

heavier one will hv less velocity so the ans is either b or c ,now what about momentum ?

Answer 8

and since the force is same for both, momentum will be equal

Answer 9

you can reconcile this even with simple
F = ma
where acceleration is the change in velocity over time.

heavier objects tend to require more force to keep up with the speed to keep up with lighter objects

Answer 10

momentum is a separate issue

Answer 11

i cannot understand why momentum is same ?

Answer 12

Because Force = Rate of change in momentum. Same force for same time will build up same momentum

Answer 13

momentum of a lighter objects that speeds up really really fast may be the same for heavier objects with slower speed

it is based on the formula you were given earlier

Answer 14

and since momentum = mass*velocity, the one with lower mass will have higher velocity and vice-versa

Answer 15

so u mean to say tht the force will be same on both the heavy and ligt objects ?

Answer 16

yes

Answer 17

\[Ma = m a _{1}\]
and M > m
then a1 > a

Answer 18

momentum (P)
P = mass * velocity

Answer 19

Got it ?

Answer 20

but see it
https://www.youtube.com/watch?v=_mCC-68LyZM

it says tht force is different !

Answer 21

you need to understand kinetic and potential energies to get a better clue how momentum works

Answer 22

you can think of it without momentum

Answer 23

see 1:32 section of this video

Answer 24

http://finedrafts.com/files/CUNY/Physics/

you can select either physics with calculus or just with algebra, the concept remains the same

Answer 25

stop watching videos and start reading textbooks first

Answer 26

ohk :)

Answer 27

I think it would be better if one person tries to make him understand at once.

Answer 28

yes please i am really confused about momentum stuff here

Answer 29

this video is saying tht they accelerate at differnt rate !

Answer 30

choices tell you about building up means acceleration
it is the same force he told you that
and that video spoke about gravitation force !!

Answer 31

start with textbooks then we can clarify them all later

start with speed/velocity, acceleration ...
it is a progression of concepts

Answer 32

acceleration at different rates has no direct bearing on momentum
because momentum depends on both the mass and velocity
two factors determine it!

Answer 33

ohk

Answer 34

it's why you need to understand other concepts like KINETIC and POTENTIAL ENERGIES first!
you will see how they beautifully fit into momentum

Answer 35

@moli1993

Force is equal to rate of change in momentum i.e Force = \(\sf \Delta mv/t\)

is this ok ?

Answer 36

\(\sf \Delta mv\) means Final momentum-initial momentum

Answer 37

So, Final momentum - initial momentum = Force*time

ok ?

Answer 38

yes

Answer 39

\[=m \Delta v \]

Answer 40

Now suppose a body is initially at rest

Answer 41

This will lead to 0 initial momentum....correct ?

Answer 42

yes

Answer 43

Now suppose F force for time t is applied on it. then its momentum will become F*T and this will be equal to product of its mass and velocity...correct ?

Answer 44

yes

Answer 45

but f*t = impulse ?

Answer 46

If we change the mass of this object [somehow] then its velocity will increase accordingly to maintain the product equal to F*t

Answer 47

\(\color{blue}{\text{Originally Posted by}}\) @moli1993
but f*t = impulse ?
\(\color{blue}{\text{End of Quote}}\)

Yes that's correct. you can also say that change in momentum= Impulse

Answer 48

why should velocity increase to maintain f*t ??

Answer 49

Because the product F*t has to be constant. that's the condition we are dealing with

Answer 50

ok ok then ?

Answer 51

\[J = \sum F (t_2 - t_1) = \sum F \Delta t\]
\[\sum F = \frac{p_2-p_1}{t_2-t_1} \rightarrow \sum F(t_2-t_1) = p_2-p_1 \rightarrow J = p_2 - p_1 \]
Impulse-momentum theorem

Answer 52

So basically, whet F*t is constant, m is inversely proportional to velocity

Answer 53

in other words, larger mass will have lower velocity and smaller mass will have larger velocity

Answer 54

and this is because the product F*t is constant which means momentum is constant. Does that make any sense to you ?

Answer 55

Impulse when force is not constant
\[\int\limits^{t_2}_{t_1} \sum F dt = \int\limits^{t_2}_{t_1}\frac{dp}{dt}dt = \int\limits^{p_2}_{p_1} dp = p_2 - p_1\]
general definition of impluse
\[J = \int\limits^{t_2}_{t_1} \sum F dt\]

Answer 56

do you get it yet?
one way to reconcile this is to solve an actual problem with varying mass and same force applied. calculate the momentum, but first you need to calculate the velocity

Answer 57

Thank u @nincompoop and @Abhisar :)